We present a differential system which generalises in degree the Cartan structural equations of Riemannian geometry. We study its main consequences in dimension 3, where the system is given by three 2-forms α0,α1,α2 defined on the contact mani- fold (SM3,θ) which is the 2-sphere tangent bundle of any given oriented Riemannian 3-manifold M 3 . This intrinsic structure of Riemannian geometry relates to Conti- Salamon hypo structures and may be developed as an odd-dimensional version of twistor geometry. We also show the construction, through the same structural equations, of a natural G2 structure on SM4 for any given oriented Riemannian 4-manifold.